The celestial mechanics approach: application to data of the GRACE mission

The celestial mechanics approach (CMA) has its roots in the Bernese GPS software and was extensively used for determining the orbits of high-orbiting satellites. The CMA was extended to determine the orbits of Low Earth Orbiting satellites (LEOs) equipped with GPS receivers and of constellations of LEOs equipped in addition with inter-satellite links. In recent years the CMA was further developed and used for gravity field determination. The CMA was developed by the Astronomical Institute of the University of Bern (AIUB). The CMA is presented from the theoretical perspective in (Beutler etal. 2010). The key elements of the CMA are illustrated here using data from 50 days of GPS, K-Band, and accelerometer observations gathered by the Gravity Recovery And Climate Experiment (GRACE) mission in 2007. We study in particular the impact of (1) analyzing different observables [Global Positioning System (GPS) observations only, inter-satellite measurements only], (2) analyzing a combination of observations of different types on the level of the normal equation systems (NEQs), (3) using accelerometer data, (4) different orbit parametrizations (short-arc, reduced-dynamic) by imposing different constraints on the stochastic orbit parameters, and (5) using either the inter-satellite ranges or their time derivatives. The so-called GRACE baseline, i.e., the achievable accuracy of the GRACE gravity field for a particular solution strategy, is established for the CM

The celestial mechanics approach: theoretical foundations

Gravity field determination using the measurements of Global Positioning receivers onboard low Earth orbiters and inter-satellite measurements in a constellation of satellites is a generalized orbit determination problem involving all satellites of the constellation. The celestial mechanics approach (CMA) is comprehensive in the sense that it encompasses many different methods currently in use, in particular so-called short-arc methods, reduced-dynamic methods, and pure dynamic methods. The method is very flexible because the actual solution type may be selected just prior to the combination of the satellite-, arc- and technique-specific normal equation systems. It is thus possible to generate ensembles of substantially different solutions—essentially at the cost of generating one particular solution. The article outlines the general aspects of orbit and gravity field determination. Then the focus is put on the particularities of the CMA, in particular on the way to use accelerometer data and the statistical information associated with i

Variance component estimation for co-estimated noise parameters in GRACE Follow-On gravity field recovery

Temporal gravity field modelling from GRACE Follow-On deals with several noise sources polluting the observations and the system of equations, be it actual measurement noise or mis-modellings in the underlying background models. One way to collect such deficiencies is to co-estimate additional pseudo-stochastic parameters in the least-squares adjustment which are meant to absorb any kind of noise while retaining the signal in the gravity field and orbit parameters. In the Celestial Mechanics Approach (CMA) such pseudo-stochastic parameters are typically piece-wise constant accelerations set up in regular intervals of e.g., 15 min, and an empirically determined constraint is added to confine the impact of the additional quantities. As the stochastic behaviour of these parameters is unknown because they reflect an accumulation of a variety of noise sources, Variance Component Estimation (VCE) is a well established tool to assign a stochastic model to the pseudo-stochastic orbit parameters driven by the observations. In the simplest case the magnitude of the constraints of the pseudo-stochastic orbit parameters can be determined fully automatically. We present results for GRACE Follow-On gravity field recovery when extending the CMA by stochastic models for the piece-wise constant accelerations computed with VCE and provide noise and signal assessment applying the quality control tools routinely used in the frame of the Combination Service for Time-variable gravity fields (COST-G)